1. Modeling the Effect of Curvature on the Collective Behavior of Cells Growing New Tissue 
Mohd Almie Alias, Pascal R. Buenzli 
Biophysical Journal 
Volume 112, Issue 1, Pages (January 2017)
DOI: /j.bpj
Copyright © 2017 Biophysical Society Terms and Conditions

2. Figure 1
(a) Cells lining a tissue surface such as bone-forming osteoblasts will concentrate or spread during the evolution of the interface depending on whether the initial substrate is concave (κ < 0) or convex (κ > 0) (top). In a similar way, cellular and extracellular tissue volume produced near the tissue surface will crowd or spread depending on the substrate curvature (bottom). In both cases, this influences the local tissue growth rate. (b) Schematic diagram depicting the representation of the tissue surface S(t) by an arbitrary parameterization γ(s,t) and by an orthogonal parameterization Γ(u,t). Timelines of Γ(u,t) follow the cell’s trajectories assumed normal to S(t) at all times.
Biophysical Journal  , DOI: ( /j.bpj )
Copyright © 2017 Biophysical Society Terms and Conditions

3. Figure 2
Tissue deposition on a cosine initial substrate for a range of low to high diffusivities (D = , , 0.015, 1 mm2/day). (a) Evolution of the tissue interface. Each line corresponds to the interface h(x,t) at regular time intervals Δt = 8.33 days, and is colored according to cell density. (b) Cell density profiles at specific times. Simulations performed with A = 0, kf0=1, and ρ0 = 0.016 mm/day. To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
Copyright © 2017 Biophysical Society Terms and Conditions

4. Figure 3
Influence of diffusivity on the rate and manner of smoothing of an initial cosine interface. The total length of the interface transitions from damped oscillation regimens at low diffusivities, to critically damped regimens at intermediate diffusivities, to overdamped regimens at high diffusivity. (Inset) The minimum integral of the timeline t ↦ L(t) is reached at a critical diffusivity D ≈  mm2/day smaller than the critical diffusivity D ≈ 0.015 mm2/day at which oscillating patterns are lost. To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
Copyright © 2017 Biophysical Society Terms and Conditions

5. Figure 4
Tissue deposition within triangular, square, and hexagonal pores (each with initial perimeter 9 mm) for low (D =  mm2/day), intermediate (D = 0.005 mm2/day), and high (D = 1 mm2/day) diffusivities. The tissue interface is shown at regular time intervals Δt = 2.6 days until t = 26 days and colored according to cell density. Simulations performed with A = 0, kf0=1, and ρ0 = 0.016 mm/day. To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
Copyright © 2017 Biophysical Society Terms and Conditions

6. Figure 5
Tissue deposition predicted by our cell-based model with Eq. 12 in the bioscaffold pore shapes of Bidan et al. (25) (circular and semicircular pore shapes) and Bidan et al. (26) (square and cross pore shapes). (a) The tissue interface is shown at days 4, 7, 14, and 21 and colored according to cell density. (b) The time evolution of the total tissue area produced AT(t) (normalized by the initial pore area in the circular and semicircular cases) is shown for various values of diffusivity D and cell elimination rate A. These time evolutions are compared with the experimental results and simulations of the phenomenological model of Bidan et al. (25,26). To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
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7. Figure 6
Evolution of the tissue interface of the cell-based model in the semicircular (top) and cross (bottom) interfaces with some of the combinations of A and D that were used in Fig. 5 b. The tissue interface is shown at days 7, 14, and 21 and colored according to cell density. Left column: experimental bioscaffold tissue growth showing the extent of new tissue at days 7 (red), 14 (orange), and 21 (yellow). Semi-circular pore image: reproduced with permission from Bidan et al. (25). Cross pore image: Copyright Wiley-VCH Verlag GmbH & Co. KGaA. Reproduced with permission from Bidan et al. (26). To see this figure in color, go online.
Biophysical Journal  , DOI: ( /j.bpj )
Copyright © 2017 Biophysical Society Terms and Conditions